1
IIT-JEE 2004 Screening
+3
-0.75
If $$f(x)$$ is differentiable and $$\int\limits_0^{{t^2}} {xf\left( x \right)dx = {2 \over 5}{t^5},}$$ then $$f\left( {{4 \over {25}}} \right)$$ equals
A
$$2/5$$
B
$$-5/2$$
C
$$1$$
D
$$5/2$$
2
IIT-JEE 2003 Screening
+3
-0.75
If $$l\left( {m,n} \right) = \int\limits_0^1 {{t^m}{{\left( {1 + t} \right)}^n}dt,}$$ then the expression for $$l(m, n)$$ in terms of $$l(m+n, n-1)$$ is
A
$${{{2^n}} \over {m + 1}} - {n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
B
$${n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
C
$${{{2^n}} \over {m + 1}} + {n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
D
$${m \over {n + 1}}l\left( {m + 1,n - 1} \right)$$
3
IIT-JEE 2003 Screening
+3
-0.75
The area bounded by the curves $$y = \sqrt x ,2y + 3 = x$$ and
$$x$$-axis in the 1st quadrant is
A
$$9$$
B
$$27/4$$
C
$$36$$
D
$$18$$
4
IIT-JEE 2003 Screening
+3
-0.75
If $$f\left( x \right) = \int\limits_{{x^2}}^{{x^2} + 1} {{e^{ - {t^2}}}} dt,$$ then $$f(x)$$ increases in
A
$$(-2, 2)$$
B
no value of $$x$$
C
$$\left( {0,\infty } \right)$$
D
$$\left( { - \infty ,0} \right)$$
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